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On the NP-Hardness of Two Scheduling Problems Under Linear Constraints

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Frontiers of Algorithmics (IJTCS-FAW 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13933))

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Abstract

In this work, we investigate the computational complexity of two different scheduling problems under linear constraints, including single-machine scheduling problem with total completion time and no-wait two-machine flow shop scheduling problem. In these problems, a set of jobs must be scheduled one or more machines while the processing times of them are not fixed and known in advance, but are required to be determined by a system of given linear constraints. The objective is to determine the processing time of each job, and find the schedule that minimizes a specific criterion, e.g., makespan or total completion time among all the feasible choices. Although the original scheduling problems are polynomially solvable, we show that the problems under linear constraints become NP-hard. We also propose polynomial time exact or approximation algorithms for various special cases of them. Particularly, we show that when the total number of constraints is a fixed constant, both problems can be solved in polynomial time by utilizing the scheduling algorithms and the properties of linear programming.

This research work is partially supported by the Natural Science Foundation of Fujian Province of China No. 2021J05011 and the Fundamental Research Funds for the Central Universities of Xiamen University No. 20720210033.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, China

    Kameng Nip

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  1. Kameng Nip
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Correspondence to Kameng Nip .

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Editors and Affiliations

  1. City University of Hong Kong, Hong Kong SAR, China

    Minming Li

  2. Chinese Academy of Sciences, Beijing, China

    Xiaoming Sun

  3. University of Macau, Macau, China

    Xiaowei Wu

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Nip, K. (2023). On the NP-Hardness of Two Scheduling Problems Under Linear Constraints. In: Li, M., Sun, X., Wu, X. (eds) Frontiers of Algorithmics. IJTCS-FAW 2023. Lecture Notes in Computer Science, vol 13933. Springer, Cham. https://doi.org/10.1007/978-3-031-39344-0_5

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  • DOI: https://doi.org/10.1007/978-3-031-39344-0_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-39343-3

  • Online ISBN: 978-3-031-39344-0

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